Reference links:
What is a heuristic algorithm
definition:
General heuristics for solving NP-hard problem, which is NP refers to non-deterministic polynomial.
### with respect to the heuristic is proposed optimization algorithm, the algorithm is based on experience or intuition configuration, to be given within an acceptable overhead (time and space) of a combinatorial optimization problem solving feasible solution.
example:
- For example, the famous traveling salesman problem (Travel Saleman Problem or TSP): Suppose a salesman needs from Nanjing, through Guangzhou, Beijing, Shanghai, ..., n and other cities, and finally returned to Hong Kong. Have direct aircraft between any two cities, but fares ranging. Assuming that the company only to be reimbursed C dollars, to ask whether there is an itinerary, so that he can traverse all the cities, and the total toll is less than C?
- Traveling salesman problem is clearly the NP. Because if any of you give an itinerary, you can easily calculate the total cost of travel. However, to know a total toll of the trip if there is less than C, in the worst case, you must check all possible travel arrangements.
Current general heuristics
Simulated annealing algorithm (SA), genetic algorithms (GA), ant colony algorithm (ACO), artificial neural network (ANN) and so on.
Simulated annealing algorithm (SA)
definition:
Thought simulated annealing algorithm (Simulated Annealing, SA) reference to the principle of annealed solid, solid when the temperature is high when the internal energy is relatively large, solid particles of internal disorder in rapid motion, when the temperature is gradually lowered in the process , the energy of the solid decreases, the particles gradually become ordered, finally, when the room temperature is a solid, to achieve the minimum time, the most stable particle. Simulated annealing algorithm is designed based on this principle.
Simulated annealing algorithm steps:
- Initialization temperature T (sufficiently large), the lower temperature limit of Tmin (sufficiently small), the initial solution X, number of iterations for each value of T L
- Randomly generated temporary domain solution x_new;
- Provided f (x) function is calculated for calculating the good or bad solutions, the calculated f (x_new) -f (x);
- If f (x_new) -f (x)> 0, a good description of the new solutions of the original solution than the accepted unconditionally, if f (x_new) -f (x) <0, then the new solution is better than the old solution, places probability exp ((f (xnew) -f (x)) / k * T) x_new accepted as a solution.
- If the current temperature <Tmin, exit loop, the output current result, or decreases the current temperature, the cycle continues back to step 2, conventional cooling method T = a * T (0 <a <1), generally taking a close value of 1
Genetic Algorithms (GA)
definition:
Genetic Algorithms (Genetic Algorithm, GA) originated in the computer simulation of biological systems carried out. Random global search and optimization methods which mimic the natural biological evolution mechanism developed, drawing on Darwinian evolution and Mendelian genetics. Its essence is a highly efficient, parallel, global search method, and can automatically acquire the accumulation of knowledge about the search space in the search process and the search process is adaptively controlled in order to achieve an optimal solution.
Genetic algorithm steps
- Encoding potential problems, initialization genome and random initial population according genome, and specify the reproduction algebra.
- Calculate the population of each individual's fitness to select a certain number of leave, and the rest eliminated.
- Left in an individual, the random reproduction, crossover denominator genes (small probability variation), the next generation.
- Go back to step 2 cycle. Until it reaches a specified multiply algebraic
Ant colony algorithm (ACO)
definition:
- We try to recover what ants looking for food scene.
- Imagine an ant find a food, then it needs to be brought back to the nest food. For this ant is concerned, it obviously does not know how to go. So the ant there may randomly select a route.
- This route is likely to be a long journey. However, the way ants left a mark, which is the pheromone. If you continue to keep the ant carrying food, or many other ants carrying a case. They will always lucky when went back and forth on a faster route. Ants choose the better way, the number of round trips within the same time there is more, it leaves more in the way of pheromones.
- So, the ants always find some path pheromone thicker, these paths is the better route. So ants also more shifted to the more concentrated pheromone path. Ants kept repeating this process, eventually can always find a certain route, but this route is to find the optimal path of the ants.
Ant colony algorithm steps
- Initialization number of ants, viable link, each link distance, initial pheromone size information of each link
- Ants set start and end points.
- Ants from the starting point based on the pheromone concentration, there is a certain probability of selection sections, the higher the concentration, the greater the probability, gradually returned to the end.
- Ants on the path traveled, the length of each link to scale pheromone, a short segment of pheromone release, less long section of pheromone release.
- All sections were volatile pheromone.
- Back to the second step loop until the number of iterations ants finish.
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Various specific implementations of modern heuristic is relatively independent proposed, quite different from each other. Historically, modern heuristic algorithm are: simulated annealing algorithm (SA), genetic algorithms (GA), a list of search algorithm (ST), evolutionary programming (EP), evolution strategies (ES), ant colony algorithm (ACA) artificial neural network (ANN). If considered from a different coding scheme decision variable, there may be coded (static coding) and coding (dynamic code) of the fixed-length variable length two schemes. SA is a global probabilistic search algorithm Monte Carlo algorithm based on iterative solution, with features different from conventional search mechanisms and algorithms, it is to learn the principles of thermodynamics annealing built up. GA is proposed refer to the "survival of the fittest" biological evolution and the genetic a global parallel search algorithm. EP and ES unlike GA emphasis on parent and progeny contact details and focus on the behavior of parent and offspring performance (emphasis on behavior change layer species). TS is a kind of global memory function gradually optimized algorithms. ACA is one kind of people inspired by the true nature of the research results of the collective behavior of ant colony simulation proposed evolutionary algorithm based on population, belong to the random search algorithm.